Properly licensed doctors (MDs and DOs) and registered nurses (RNs) and physician's assistants (PAs) under the supervision of a doctor may inject Botox or Restylane. The degree of supervision may be the real question, however.
In some spas, nurses perform these injections for clients or patients without the direct supervision of a physician in some cases. The "supervising physician: may be nothing more than a signature on a form somewhere, for which a fee is paid by the spa to the doctor. Legal--yes; appropriate--you decide for yourself!
I'm not saying a doctor necessarily has to be right there to "supervise" a trained, experienced, skilled RN injector. BUT, any patient who has injections by such a person SHOULD know who the supervising physician is, and who is responsible if there is a complaint or concern. (see the 40% who feel it is "not worth it" on this forum.)